Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n ≥ 1, let G_n denote the complete graph of order n, and for all even integers n ≥ 2 let G_n denote the complete graph of order n with the edges of a 1‐factor removed. It is shown that for all non‐negative integers h and t and all positive integers n, G_n can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G_n. © 2004 Wiley Periodicals, Inc.